Advertisements
Advertisements
प्रश्न
Choose the correct answer from the given four options :
Which of the following equations has two distinct real roots?
पर्याय
`2x^2 - 3sqrt(2)x + (9)/(4)` = 0
x² + x – 5 = 0
`x^2 + 3x + 2sqrt(2)` = 0
5x² – 3x + 1 = 0
Advertisements
उत्तर
`2x^2 - 3sqrt(2)x + (9)/(4)` = 0
b2 - 4ac
= `(-3sqrt(2))^2 - 4 xx 2 xx (9)/(4)`
= 18 - 18
= 0
∴ Roots are real and equal.
x² + x – 5 = 0
b2 - 4ac
= (1)2 - 4 x 1 x (-5)
= 1 + 20
= `sqrt(21)` > 0
∴ Roots are real and distinct.
APPEARS IN
संबंधित प्रश्न
Find that value of p for which the quadratic equation (p + 1)x2 – 6(p + 1)x + 3(p + 9) = 0, p ≠ –1 has equal roots. Hence, find the roots of the equation.
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
`3x^2 - 4sqrt3x + 4 = 0`
In the following determine the set of values of k for which the given quadratic equation has real roots:
x2 - kx + 9 = 0
Write the discriminant of the quadratic equation (x + 5)2 = 2 (5x − 3).
Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0
Find the values of k for which each of the following quadratic equation has equal roots: 9x2 + kx + 1 = 0 Also, find the roots for those values of k in each case.
The sum of the roots of the quadratic equation 3x2 – 9x + 5 = 0 is:
(x2 + 1)2 – x2 = 0 has ______.
The sum of all integral values of k(k ≠ 0) for which the equation `2/(x - 1), 1/(x - 2) = 2/k` in x has no real roots, is ______.
If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is ______.
